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Questions and Answers
What is the property of an equation that states that if a = b, then b = a?
What is the property of an equation that states that if a = b, then b = a?
Which of the following equations is a quadratic equation?
Which of the following equations is a quadratic equation?
What is the purpose of the Inverse Operations method in solving equations?
What is the purpose of the Inverse Operations method in solving equations?
What is the result of applying the Addition/Subtraction Property to both sides of the equation 2x + 3 = 5?
What is the result of applying the Addition/Subtraction Property to both sides of the equation 2x + 3 = 5?
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Which of the following is an example of a linear equation?
Which of the following is an example of a linear equation?
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What is the result of applying the Multiplication/Division Property to both sides of the equation 2x = 6?
What is the result of applying the Multiplication/Division Property to both sides of the equation 2x = 6?
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Study Notes
Equations
Definition
- An equation is a statement that says two mathematical expressions are equal.
- It is denoted by the equality symbol (=).
Types of Equations
-
Simple Equations: Equations in which the highest power of the variable(s) is 1.
- Example: 2x + 3 = 5
-
Quadratic Equations: Equations in which the highest power of the variable(s) is 2.
- Example: x^2 + 4x + 4 = 0
-
Linear Equations: Equations in which the highest power of the variable(s) is 1, and can be written in the form ax + by = c.
- Example: 2x + 3y = 7
Properties of Equations
- Reflexive Property: a = a (an equation is equal to itself)
- Symmetric Property: if a = b, then b = a (equations can be swapped)
- Transitive Property: if a = b and b = c, then a = c (equations can be chained)
Solving Equations
- Addition/Subtraction Property: adding or subtracting the same value to both sides of an equation does not change its solution.
- Multiplication/Division Property: multiplying or dividing both sides of an equation by a non-zero value does not change its solution.
-
Inverse Operations: using opposite operations to isolate the variable(s).
- Example: 2x = 6 → x = 6/2 → x = 3
Equations
Definition
- An equation is a statement that says two mathematical expressions are equal, denoted by the equality symbol (=).
Types of Equations
Simple Equations
- Equations in which the highest power of the variable(s) is 1.
- Example: 2x + 3 = 5
Quadratic Equations
- Equations in which the highest power of the variable(s) is 2.
- Example: x^2 + 4x + 4 = 0
Linear Equations
- Equations in which the highest power of the variable(s) is 1, and can be written in the form ax + by = c.
- Example: 2x + 3y = 7
Properties of Equations
Reflexive Property
- An equation is equal to itself (a = a).
Symmetric Property
- If a = b, then b = a (equations can be swapped).
Transitive Property
- If a = b and b = c, then a = c (equations can be chained).
Solving Equations
Addition/Subtraction Property
- Adding or subtracting the same value to both sides of an equation does not change its solution.
Multiplication/Division Property
- Multiplying or dividing both sides of an equation by a non-zero value does not change its solution.
Inverse Operations
- Using opposite operations to isolate the variable(s).
- Example: 2x = 6 → x = 6/2 → x = 3
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Description
Learn about the definition and types of equations, including simple, quadratic, and linear equations. Understand the concept of equality and powers of variables.
